Answer to Question #148776 in Quantum Mechanics for Max

Question

What is energy of harmonic oscillator.

Answer 1

In the absence of dissipative forces, the total mechanical energy of a simple harmonic oscillator is constant and proportional to the square of the amplitude:

$E = \frac{1}{2}kA^2$

where the potential energy has been chosen to be zero at the equilibrium point. At any point, the sum of the kinetic and potential energies is constant:

$E = \frac{1}{2}mv_x^2 + \frac{1}{2}kx^2 = \frac{1}{2}kA^2$